Question: Why minimize returns wrong minimum?

Let x, y, z be nonnegative real numbers. Obviously, x3+y3+z3-4xyz is not always nonnegative, since its value is -1 when x=y=z=1. But why Maple's minimize gives wrong result? 

minimize(x^3 + y^3 + z^3 - 4*x*y*z, x = 0 .. infinity, y = 0 .. infinity, z = 0 .. infinity);

Attachment: MinValue.mws.

MMA's Minimize finds correct infimum: 
So, can Maple always find correct exact (i.e., not just numerical) global minima (or maxima) at least for such problems with a small number of variables as well?

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